COLLOQUE 2015

Le premier colloque "Rituals, Mathematics & the Astral Sciences" a eu lieu à Paris les 19 & 20 mars 2015 à l'Université Paris Diderot, Paris.

Organisateurs : Karine CHEMLA (CNRS, SPHERE, & SAW Project),  Sho HIROSE (Université Paris Diderot, SPHERE, & SAW Project), Agathe KELLER (CNRS, SPHERE, & SAW Project) et Daniel P. MORGAN (CNRS, SPHERE, & SAW Project)

Télécharger le livret 2015 & 2016: Booklet_RitualMathematicsAstralSciences_SAW_2016

PROGRAMME 2015

RÉSUMÉS 2015

YANO Michio    | Kyoto Sangyo University, Japan

Astral sciences & rituals in India with reference to ayana

 Commentaire : Daniel P. MORGAN |
CNRS, SPHERE, & SAW project, Paris

The very primitive system of the Jyotiṣavedāṅga turned to a well-established branch of science, namely, jyotiḥśāstra (‘‘science of stars’’), and it made remarkable progress, especially after the introduction of western astronomy and astrology. We see a drastic change of Indian astrology after the Yavanajātaka was translated into Sanskrit some time around the 3rd or 4th century CE. Moreover, after the Āryabhaṭīya of Āryabhaṭa numerous texts on mathematical astronomy were produced until a quite recent time.  Although the five year cycle (yuga) of the Jyotiṣavedāṅga was very crude, basic units of time were defined, namely, year, half year (ayana), month, half month (pakṣa), tithi, muhūrta (1/30 of a day), and nāḍikā (1/60 of a day). The meaning of ayana in the context of ritualism, astronomy and astrology changed in history. At the time of Jyotiṣavedāṅga the word ayana only meant ‘a half year’, a year being divided into two, uttara-ayaṇa (‘sun’s northern course’) and dakṣina-ayana (‘sun’s southern course’). With time, however, the change of the position of the solstices became known to Indian astronomers, and ayanāṣśa (degrees of motion of solstices) became an important topic. In the nirayaṇa (sidereal) system, planetary longitudes are counted from the fixed ecliptic point meṣādi (the beginning of Meṣa) while according to the sāyana (tropical) system, the starting point of reference is the true vernal equinox.  When one wants to compute the astronomical elements called vyatīpāta and vaidhṛta which are defined by the true decli-nation of the sun and the moon, one must use the sāyana coordinates, while the yoga, as one of the five astrological elements, is computed by the nirayaṇa system. The majority of traditional Indian calendars (pañcāṅga) give the planetary position in the nirayaṇa system.
Whether Indian calendars should continue to use the nirayaṇa system or switch to the sāyana system is a big issue among the traditional calendar makers and ritualists.
 

Bill MAK   | Kyoto Sangyo University, Japan

Ritualistic cyclicity in Indo-Greek astral science
– Expressions for various modes of time measurement in the Yavanajātaka

 Commentaire : Daniel P. MORGAN |
CNRS, SPHERE, & SAW project, Paris

As a prototypical work of Greco-Indian astral science, the Yavanajātaka, in particular, its last chapter (Ch. 79) on mathematical astronomy, encapsulates some key concepts on time measurements which would later became the mainstream elements in the Indian tradition of jyotiṣa. Some of these key concepts include the large astronomical cycle known as yuga, the smaller cycles of year, season, month, planetary week, day and tithi. What distinguishes the Yavanajātaka from other extant treatises of the first millennium CE, however, is the fluidity of expression of these astronomical cycles in the text, which suggests the ambivalence of the author in his attempt to blend a heterogeneous body of Greek and Indian astronomical and astral concepts, and to express them in a sound, mathematical manner. Two features of this important chapter which have been overlooked in past studies are: 1) The Indian elements as exemplified by the close resemblance of tithi-based astronomical algorithm and the description of the water clock to those of the Vedāṅgajyotiṣa and the Arthaśāstra respectively;
2) The description of the Lords of year, ayana, season, month, week, day and hour which conclude the chapter before the colophon. In this presentation, I would like to suggest the expressions of cyclical time-measures in the text have an unexpressed ritualistic character, which lies beyond the scope of the Greco-Indian genethliacal astrology of the preceding 78 chapters. Beside his concern for comprehensiveness, its author Sphujidhvaja was clearly exposed to the ritualistic significance of these various time-measures from different traditions. While the computation of planetary longitude would be essential to the casting of horoscope, the reckoning of days (ahargaṇa) and various “Lords” suggests a synthesis of Greek and Indian rituals which focus on astral worship.

1 Based on readings from new manuscript [Mak 2013]

ZHU Yiwen   | Sun Yatsen University, China, & SAW project

Commentaries on ritual numbers through different mathematical knowledges in seventh century China

 Commentaire : Sho HIROSE |
Université Paris Diderot, CNRS, SPHERE, & SAW project, Paris

 Numbers of ritual (Lishu 禮數) is a key part of ritual in ancient China. Some studies have been done on it based on ritual texts. On the other hand, Liu Hui 劉徽, who commented on the Nine Chapters on Mathematical Procedures (Jiuzhang suanshu 九章筭術), understood this book as a derivative of the Rites of Zhou (Zhouli 周禮), and further as a part of Confucianism (Ruxue 儒學). This fact points to the relationship between ritual and mathematics in general. However, it is as yet unclear how scholars in the past understood this relationship in relation to numbers of ritual. On the basis of analyzing different commentaries on numbers of ritual respectively in a mathematical book, called Mathematical Procedures on Five Canons (Wujing suanshu 五經筭術), and in Confucian canons, this talk aims at revealing different relationships between numbers of ritual and mathematical knowledges established by different scholars in seventh century China. Furthermore, the special role of numbers of ritual compared to other kind of numbers within the interdependence of ritual and mathematics will be discussed.

IKEYAMA Setsuro   | Kyoto Sangyo University, Japan

The calculation of Vyatipata, an astrological phenomenon in Indian astrology

 Commentaire : HIROSE Sho  |
Université Paris Diderot, CNRS, SPHERE, & SAW project, Paris

Vyatipata is a special, basically bad, moment in Indian astrology. It is defined in relatively later treatises as the moment when the magnitudes of the declinations of the sun and moon become equal. I will introduce the explanation and calculation of Vyatipata described in the Grahalāghava and Pāṭasāraṇī both composed by Gaṇeśa, a 16th century Indian astronomer.

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